Drawing Planar Graphs with a Prescribed Inner Face
Given a plane graph G (i.e., a planar graph with a fixed planar embedding) and a simple cycle C in G whose vertices are mapped to a convex polygon, we consider the question whether this drawing can be extended to a planar straight-line drawing of G. We characterize when this is possible in terms of simple necessary conditions, which we prove to be sufficient. This also leads to a linear-time testing algorithm. If a drawing extension exists, it can be computed in the same running time.
KeywordsPlane Graph Convex Polygon Outer Face Simple Cycle Planar Drawing
- 1.Angelini, P., Di Battista, G., Frati, F., Jelínek, V., Kratochvíl, J., Patrignani, M., Rutter, I.: Testing planarity of partially embedded graphs. In: 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2010), pp. 202–221. SIAM (2010)Google Scholar
- 7.Mchedlidze, T., Nöllenburg, M., Rutter, I.: Drawing planar graphs with a prescribed inner face. CoRR, abs/1308.3370 (2013)Google Scholar